arXiv subjects

Matthew Markowitz

Publications and source records attributed to Matthew Markowitz.

7 recordsLinked to original sources

arXiv2026

Architecture-agnostic analysis of partially coherent light with programmable photonics

The precise characterization of the spatial degree of coherence of a radiation field is important for assessing its suitability for specific applications in optical communications, advanced imaging, and quantum information processing. However, measuring the full coherence matrix traditionally requires complex, phase-sensitive interferometric setups that are highly susceptible to noise and difficult to scale on integrated platforms. To address this, we propose an architecture-agnostic approach for analyzing partially coherent light that is compatible with any universal programmable photonic unitary circuit, regardless of its internal topology. Leveraging the Schur-Horn theorem, our method diagonalizes the output coherence matrix, enabling direct extraction of its eigenvalues from output power measurements alone. We numerically validate this framework across various universal topologies and demonstrate its efficacy even in under-parameterized, non-universal architectures with only minor loss in precision. Finally, our black-box optimization approach proves inherently resilient to arbitrary optical losses and component deviations, paving the way for robust, lower-depth, and programmable spatial coherence analyzers.

physics.optics↗

arXiv2025

Universality of Photonic Interlacing Architectures for Learning Discrete Linear Unitaries

Recent investigations suggest that the discrete linear unitary group $U(N)$ can be represented by interlacing a finite sequence of diagonal phase operations with an intervening unitary operator. However, despite rigorous numerical justifications, no formal proof has been provided. Here, we show that elements of $U(N)$ can be decomposed into a sequence of $N$-parameter phases alternating with $1$-parameter propagators of a lattice Hamiltonian. The proof is based on building a Lie group by alternating these two operators and showing its completeness to represent $U(N)$ for a finite number of layers, which is numerically found to be exactly $N$. This architecture can be implemented using elementary optical components and can successfully reconstruct arbitrary unitary matrices. We propose example devices such as optical logic gates, which perform logic gate operations using a single-layer lossless and passive optical circuit design.

quant-ph↗

arXiv2025

Embedding Matrices in Programmable Photonic Networks with Flexible Depth and Width

We show that programmable photonic circuit architectures composed of alternating mixing layers and active layers offer a high degree of flexibility. This alternating configuration enables the systematic tailoring of both the network's depth (number of layers) and width (size of each layer) without compromising computational capabilities. From a mathematical perspective, our approach can be viewed as embedding an arbitrary target matrix into a higher-dimensional matrix, which can then be represented with fewer layers and larger active elements. We derive a general relation for the width and depth of a network that guarantees representing all $N \times N$ complex matrix operations. Remarkably, we show that just two such active layers, interleaved with passive mixing layers, are sufficient to universally implement arbitrary matrix transformations. This result promises a more adaptable and scalable route to photonic matrix processors.

physics.optics↗

arXiv2024

The Goldilocks Principle of Learning Unitaries by Interlacing Fixed Operators with Programmable Phase Shifters on a Photonic Chip

Programmable photonic integrated circuits represent an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Programmable photonics provides a flexible platform that can be reconfigured to perform multiple tasks, thereby holding great promise for revolutionizing future optical networks and quantum computing systems. Over the past decade, there has been constant progress in developing several different architectures for realizing programmable photonic circuits that allow for realizing arbitrary discrete unitary operations with light. Here, we systematically investigate a general family of photonic circuits for realizing arbitrary unitaries based on a simple architecture that interlaces a fixed intervening layer with programmable phase shifter layers. We introduce a criterion for the intervening operator that guarantees the universality of this architecture for representing arbitrary $N \times N$ unitary operators with $N+1$ phase layers. We explore this criterion for different photonic components, including photonic waveguide lattices and meshes of directional couplers, which allows the identification of several families of photonic components that can serve as the intervening layers in the interlacing architecture. Our findings pave the way for efficiently designing and realizing novel families of programmable photonic integrated circuits for multipurpose analog information processing.

physics.optics↗

arXiv2023

Learning Arbitrary Complex Matrices by Interlacing Amplitude and Phase Masks with Fixed Unitary Operations

Programmable photonic integrated circuits represent an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Considering their wide range of applications as one of the most fundamental mathematical operations there has been a particular interest in programmable photonic circuits that perform matrix-vector multiplication. In this regard, there has been great interest in developing novel circuit architectures for performing matrix operations that are compatible with the existing photonic integrated circuit technology which can thus be reliably implemented. Recently, it has been shown that discrete linear unitary operations can be parameterized through diagonal phase parameters interlaced with a fixed operator that enables efficient photonic realization of unitary operations by cascading phase shifter arrays interlaced with a multiport component. Here, we show that such a decomposition is only a special case of a much broader class of factorizations that allow for parametrizing arbitrary complex matrices in terms of diagonal matrices alternating with a fixed unitary matrix. Thus, we introduce a novel architecture for physically implementing discrete linear operations. The proposed architecture is built on representing an $N \times N$ matrix operator in terms of $N+1$ amplitude-and-phase modulation layers interlaced with a fixed unitary layer that could be implemented via a coupled waveguide array. The proposed architecture enables the development of novel families of programmable photonic circuits for on-chip analog information processing.

physics.optics↗

arXiv2023

Auto-calibrating Universal Programmable Photonic Circuits: Hardware Error-Correction and Defect Resilience

It is recently shown that discrete $N\times N$ linear unitary operators can be represented by interlacing $N+1$ phase shift layers with a fixed intervening operator such as Discrete Fractional Fourier Transform (DFrFT). Here, we show that introducing perturbations to the intervening operations does not compromise the universality of this architecture. Furthermore, we show that this architecture is resilient to defects in the phase shifters as long as no more than one faulty phase shifter is present in each layer. These properties enable post-fabrication auto-calibration of such universal photonic circuits, effectively compensating for fabrication errors and defects in phase components.

cs.ET↗

arXiv2023

Universal Unitary Photonic Circuits by Interlacing Discrete Fractional Fourier Transform and Phase Modulation

We introduce a novel parameterization of complex unitary matrices, which allows for the efficient photonic implementation of arbitrary linear discrete unitary operators. The proposed architecture is built on factorizing an $N \times N$ unitary matrix into interlaced discrete fractional Fourier transforms and $N$-parameter diagonal phase shifts. We show that such a configuration can represent arbitrary unitary operators with $N+1$ phase layers. We discuss a gradient-based algorithm for finding the optimal phase parameters for implementing a given unitary matrix. By increasing the number of phase layers beyond the critical value of $N+1$, the optimization consistently converges faster as the system becomes over-determined. We propose an integrated photonic circuit realization of this architecture with coupled waveguide arrays and reconfigurable phase modulators. The proposed architecture can pave the way for developing novel families of programmable photonic circuits for optical classical and quantum information processing.

physics.optics↗